There are various processes or means for producing yarns by drafting a sliver or roving. The most general process for forming yarns comprises rotating a heavy package inserted into a spindle so as to give a true twist to a continuous bundle of short fibers. Such processes include for example ring spinning, mule spinning and flyer spinning. The spinning speed of these spinning processes is theoretically at most 30 m/min and a higher speed is not expected. On the other hand, the open-end spinning, which comprises temporarily breaking the continuity of the bundle of short fibers and feeding fibers one after another to the end of a yarn which has been already formed, while twisting the yarn, is being spotlighted. This process is now largely employed for production because of its higher productivity as compared with the former. By this process, however, the production of fine count yarns is difficult and the spinning speed remains at 2-3 times that of the former. Thus this process has not yet reached the stage of innovation. Recently, various proposals have been made on processes for producing yarns by utilizing false twist, without breaking the fiber bundle. It is well known that the productivity of these processes is markedly high in comparison with the ring spinning process. Representative of such processes is U.S. Pat. No. 3,079,746 (Fasciated Yarn Process and Apparatus for Producing the same) published on Mar. 5, 1963. As seen from its Examples, the spinning speed in the case of synthetic fibers is 914 m/min, showing a sufficient novelty indeed, but when cotton for example is used, the speed is as low as 36.6 m/min. Deviated from spinning processes of yarns, U.S. Pat. No. 3,427,647 (Wrapped Yarn Product and Process for Preparing Wrapped Yarns) published on Feb. 11, 1969 discloses a process for producing peculiar yarns. This process, intended to obtain an extremely thick covered yarn for use in non-textile fields, comprises wrapping a single filament yarn or a plurality of filament yarns around a plurality of yarns or filament yarns over nearly the whole periphery, with the twisting step being replaced with a false twist step. Anyway, there has not yet appeared any high speed spinning technique of a bundle of short fibers in the form of fleece. In the twisting or yarn forming step in both above-mentioned patents, a false twist apparatus utilizing air equipped with two air nozzles is used.